Mechanical Advantage & Simple Machines Control Power CVHS

6 Simple Machines Pulley Lever Wedge Inclined Plane Wheel & Axle Screw

The Inclined Plane Often referred to as a 'ramp' the inclined plane allows you to multiply your force over a longer distance. You do the same amount of work, it just seems easier because you spread it over time.

The Wedge A wedge works in a similar way to the inclined plane, only it is forced into an object to prevent it from moving or to split it into pieces. An axe is a common use of the wedge.

The Screw The screw is really just an inclined plane wrapped around a rod. It too can be used to move a load (like a corkscrew) or to 'split' and object (like a carpenter's screw).

The Lever The lever is simply a bar supported at a single point called the fulcrum. The positioning of the fulcrum changes the mechanical advantage of the lever. With the fulcrum positioned closer to the load, you can exert less force over a longer distance.

The Wheel & Axle Any large disk (wheel) attached to a small diameter shaft or rod (axle) can give you mechanical advantage. Turning a screw with a screwdriver is a simple example of a wheel and axle.

The Pulley A pulley is any rope or cable looped around a support. A very simple pulley system would be a rope thrown over a branch to hoist something into the air. Often, pulleys incorporate a wheel and axle system to reduce the friction on the rope and the support.

Mechanical Advantage (MA) Simple machines are used to reduce the force or torque needed to accomplish a given task. (When output force is gained, distance is lost) MA is a factor of how much the input force/ torque is amplified in the output of the machine.

Ideal Mechanical Advantage (IMA) This is a theoretical number. It assumes that power in = power out In other words, efficiency = 100% When you calculate MA, you will actually be finding IMA

Actual Mechanical Advantage (AMA) This is a real world number. In the real world, frictional losses prevent 100% efficiency as some of the input energy is lost in the form of heat. To find AMA, measure power in and measure power out. Then calculate MA.

IMA example The top surface of a ramp is 10 ft long. The highest point of the ramp is 5 ft off the ground. What is the IMA of the ramp

Levers Levers are classified by the location of their pivot, load, and force MA of levers is calculated by finding the distance from the load to the pivot, and the distance from the force to the pivot MA = Dist from force/ Dist from Load First Class Second Class Third Class

Calculating MA of Pulley systems A single pulley attached to a ceiling has a MA of 1 (only useful to change direction of pull) If that pulley is attached to the load (you are pulling up) the MA becomes 2 (1/2 as much force but twice the distance input). Each additional pulley you add increases the MA. The quickest way to calculate MA is to count the number of ropes (except for the last one if you are pulling it down).

Gears A gear is like a lever attached to an axle. Each tooth acts like a lever, so when a tooth of one gear contacts a tooth of a different gear, it either increases or decreases the input force.

Gearing Small gear drives large gear: Large gear drives small gear: Output speed decreases Output force increases Example: Wench, Starter, or Car Differential Large gear drives small gear: Output speed increases Output force decreases Example: Bicycle Gearing can be used to control speed and torque Use a tooth # of 1 for any worm gears.

Calculating the MA of Gears Example: 10 tooth Input gear 30 Tooth output gear MA = output/ input MA = 30/10 MA = 3:1 MA = 3 X the torque, 1/3 the speed output

Calculating the MA of Gears To calculate the total MA of gears in series, simply use the input and output (first & last) gears in you MA equation. 5t 10t 20t 5t 10t 5t

Calculating the MA of Gears When compound gear sets (or cluster gears) are used; find the MA of the first set, then find the MA of the next set, and multiply them together. First set:48/8 Ma = 6:1 Second set:48/8 MA = 6:1 6:1 x 6:1 = Total MA = 36:1

Using gears to change speed The number of teeth on a gear, and its rotational speed are directly related Formula: #of teeth in gear 1 X speed of gear 1 = #of teeth in gear 2 X speed of gear 2 Example: What output gear would be needed to reduce the speed of a 25 tooth drive gear spinning at 1000 RPM to an output speed of 500 RPM? 25x1000 = ?x500 25000/500 =50 teeth